Stochastic Stabilization of Markovian Jump Systems with State and Input Delays

This paper is concerned with the stochastic stabilizability problem of Markovian jump systems with state and input delays. For differentiable time-varying delays in each system modes of operation, a upperbound of time delay is provided, under which the delayed system retains its stochastic stabilizability if the corresponding delay-free system is stochastic stabilizable. For constant delays in each system modes of operation, delay-dependent sufficient conditions are proposed to guarantee the stochastic stabilizability of such systems.

[1]  Jong Hae Kim,et al.  Robust control for parameter uncertain delay systems in state and control input , 1996, Autom..

[2]  K. Gu An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Zhi-Hong Guan,et al.  Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays , 2003, IEEE Trans. Autom. Control..

[4]  Wook Hyun Kwon,et al.  Robust stabilization of uncertain input-delayed systems using reduction method , 2001, Autom..

[5]  Z. Artstein Linear systems with delayed controls: A reduction , 1982 .

[6]  Zidong Wang,et al.  Nonlinear filtering for state delayed systems with Markovian switching , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[7]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[8]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[9]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[10]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[11]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[12]  Wook Hyun Kwon,et al.  Feedback stabilization of linear systems with delayed control , 1980 .

[13]  Dong Yue,et al.  Robust stabilization of uncertain systems with unknown input delay , 2004, Autom..

[14]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

[15]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[16]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[17]  Wei Xing Zheng,et al.  On improved robust stabilization of uncertain systems with unknown input delay , 2006, Autom..

[18]  Andreas Antoniou,et al.  A near-optimal multiuser detector for DS-CDMA systems using semidefinite programming relaxation , 2003, IEEE Trans. Signal Process..

[19]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..